Simple regression models

Fitting and assessing simple models

Jonathan Binder
jonathan.binder.2022@live.rhul.ac.uk

Royal Holloway, University of London

16 Feb 2026

What is a model?

Bin im Garten, CC BY-SA 3.0, via Wikimedia Commons

Adrian Pingstone - arpingstone (talk)., Public domain, via Wikimedia Commons

Statistical models

  • mathematical representation of phenomena
  • models consist of dependent variable (outcome) and one or more independent variable (predictor)
  • y = model + error

Linear model assumptions

  • linear relationship between predictor and outcome - an increase in x is associated with a proportional increase in y no matter the value of x

Linear model assumptions

  • independence of errors (no repeated measures/time series, no spatial autocorrelation, etc.)
  • homoscedasticity (constant variance) of the errors - the variance of the errors is the same across all values of x

  • errors are normally distributed